Wavelet packets-based high-resolution spectral estimation

In this paper, a new scheme of sinusoidal components frequency estimation is proposed. One of the innovations presented is that the estimation is performed on a subband decomposition of the signal. To minimize some of the drawbacks of a rigid filter bank, the decomposition is made adaptive using wavelet packets optimizing a new criterion. Thereafter, a high-resolution estimation technique is applied in the subbands. The new criterion consists in counting the number of modes contained in the subbands using the minimum description length (MDL) criterion, derived from the Akaike information criterion. The optimal subband decomposition is found by maximizing the number of modes over the decomposition tree. This causes the decomposition to stop when a mode will be aliased. The adaptive subband decomposition guarantees the benefits of estimation from a subband decomposition without the inconveniences of the aliasing effects. Simulations performed on synthetic signals confirmed the gain in performance of the proposed method.